Categorical Semantics of Cyber-Physical Systems Theory

Abstract

Cyber-physical systems require the construction and management of various models to assure their correct, safe, and secure operation. These various models are necessary because of the coupled physical and computational dynamics present in cyber-physical systems. However, to date the different model views of cyber-physical systems are largely related informally, which raises issues with the degree of formal consistency between those various models of requirements, system behavior, and system architecture. We present a category-theoretic framework to make different types of composition explicit in the modeling and analysis of cyber-physical systems, which could assist in verifying the system as a whole. This compositional framework for cyber-physical systems gives rise to unified system models, where system behavior is hierarchically decomposed and related to a system architecture using the systems-as-algebras paradigm. As part of this paradigm, we show that an algebra of (safety) contracts generalizes over the state of the art, providing more uniform mathematical tools for constraining the behavior over a richer set of composite cyber-physical system models, which has the potential of minimizing or eliminating hazardous behavior.

References in corpus (13)

• Quantum Picturalism
• The operad of wiring diagrams: formalizing a graphical language for databases, recursion, and plug-and-play circuits
• Compositional Synthesis via a Convex Parameterization of Assume-Guarantee Contracts
• Algebras of Open Dynamical Systems on the Operad of Wiring Diagrams
• The operad of temporal wiring diagrams: formalizing a graphical language for discrete-time processes
• Co-Design to Enable User-Friendly Tools to Assess the Impact of Future Mobility Solutions
• On the Co-Design of AV-Enabled Mobility Systems
• Compositional Cyber-Physical Systems Modeling
• Parallel Composition and Modular Verification of Computer Controlled Systems in Differential Dynamic Logic
• The steady states of coupled dynamical systems compose according to matrix arithmetic
• Compositional Models for Power Systems
• Reachability analysis of linear hybrid systems via block decomposition
• Formal composition of hybrid systems

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• An Algebraic Framework for Structured Epidemic Modeling
• Compositional Thinking in Cyberphysical Systems Theory
• Characterizing Compositionality of LQR from the Categorical Perspective